Research On Signatures Based On NTRU

With the fast development of the networks as well as the appearance of more and more information systems dealing with governmental affairs, commercial affairs, and even daily affairs, digital signature - a subset of public-key cryptology -is sure to be attractive for more extensive applications in the coming years. The relations between digital signature and digital document are similar to those between typical written signature and paper document. As a result, digital signature has been widely used in E-Government and E-Commerce. Since the idea of "digital signature" was firstly proposed by W.Diffie and M.Hellman, many digital signatures have been proposed, such as the famous schemes of RSA, ElGamal, DSS, etc.NTRU Cryptosystem is an important subject in the field of modern public key cryptography, and it is a new simple public key cryptography of expeditiousness. The security of the NTRU Public Key Cryptosystem is based on the hard problem of finding a very short vector in a lattice of very high dimension. This arithmetic can be One-Time Pad because of its terriblely high speed of encryption, high security, and extremely ease of computing its secret key. NTRU Cryptosystem has these good characters, and been acknowledged prevalently. So it has wide application prospect in information security field. Well then, the schemes of signature based on this cryptosystem are gained high attentions.This paper below maily discusses several aspects aim at the signature schemes based on NTRU: NTRU is a PKC based on the problem of Lattice, so in chapter three, the concept and property of lattice and some hard problems of lattice (SVP(the shortest vector problem),CVP(the closest vector problem)and SBP(the smallest basis problem)) are researched. And two methods of reducing the lattice base-Gauss algorithm and LLL algorithm are also introduced. In the end of this chapter,we presents the NTRU arithmetic in detail,and the methods of attack NTRU. And we especially introduced the lattice based attacks in this charpter.The old signatures schemes based on NTRU-NSS, NTRUSign and Melleabilty of NTRUSign are discussed. In this chapter, we proposed a new signature base on NTRU, adapting secret has been specially disposed, and security is not descend. At last it was carried out it with the Mathematica. At the last, we also proposed a threshold signature based on NTRU.This is the first time combined between NTRU and secret sharing.